obtained by removing a point from a hyperoval are projectively equivalent if and only if the removed points are in the same orbit of the automorphism group of the hyperoval. There are only three small examples (in the Desarguesian planes) where the automorphism group of the hyperoval is transitive on its points so, in general, there are different types of ovals contained in a single hyperoval.

Desarguesian Case: PG(2,2^h)

This is the most studied case and so the most is known about these hyperovals.

Every nonsingular

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